Question

find the zeros of quadratic polynomial
x² +4x - 21 and verify the relationship between zeros and coefficient​

Answer 1

Answer:

3

Step-by-step explanation:

3*3+4*3-21=0 so 3 is on of zeros

Answer 2

Given polynomial:

$\implies \rm p(x) = x^2 + 4x - 21$

$\blue{\texttt{To find the zero of the given}} \\ \blue{\texttt{polynomial,}}$

$\red{\textsf{We will factorise the given equation}}$

$\rm \implies x^2 + 4x - 21 \\ \implies x^2 + 7x - 3x - 21 \\ \implies x^2 + 7x - 3x - 3 \times 7 \\ \implies x(x + 7) - 3(x + 7) \\ \implies \bold{(x - 3) (x + 7)}$

So, Now

$\sf x - 3 = 0 \\ \implies \bold{x = 3} \\ x + 7 = 0 \\ \implies \bold{ x = -7}$

Hence, the zeroes of the given polynomial are, 3 and -7.

Verification of relationship between zeroes and coefficients,

$\implies \green{\texttt{Sum of zeroes}}$

$= 3 + (-7) = -4 = \frac{-4}{1} \\ =\frac{Coefficient \: of \: x}{Coefficient \: of \: x^2}$

$\implies \green{\texttt{Product of zeroes}}$

$= 3 \times (-7) = -21 = \frac{-21}{1}\\ = \frac{Constant \: term}{Coefficient \: of \: x^2}$

Hence, Relation is Verified.